1,720,989 research outputs found
Optimal Control and viscosity solutions of Hamilton-Jacobi-Bellman equations. 2nd printing
No full textA Qualitative Phragmén–Lindelöf Theorem for Fully Nonlinear Elliptic Equations
No full textWe establish qualitative results of Phragmén–Lindelöf type for upper semicontinuous viscosity solutions of fully nonlinear partial differential inequalities of the second order in general unbounded domains of Rn, satisfying some measure-geometric property, but not necessarily regularity conditions. In particular, as for the Laplace equation, assuming elliptic structure conditions, the maximum principle holds in cylindrical and conical domains, provided that the solutions are supposed to have at most, respectively, an exponential or a polynomial growth
The Alexandrov-Bakelman-Pucci weak Maximum Principle for fully nonlinear equations in unbounded domains
No full textWe obtain Alexandrov-Bakelman-Pucci type estimates for semicontinuous viscosity solutions of fully nonlinear elliptic inequalities in unbounded domains. Under suitable assumptions relating the geometry of the domain with structural conditions on the differential operator, we establish the validity of the weak maximum principle for solutions which are bounded from above. Two variants are also given, namely one for unbounded solutions in narrow domains and one for operators with possibly changing sign zero order coefficients in domains of small measure
Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations
No full textThis book is a self-contained account of the theory of viscosity solutions for first-order partial differential equations of Hamilton–Jacobi type and its interplay with Bellman’s dynamic programming approach to optimal control and differential games, as it developed after the beginning of the 1980s with the pioneering work of M. Crandall and P.L. Lions.
The book will be of interest to scientists involved in the theory of optimal control of deterministic linear and nonlinear systems. In particular, it will appeal to system theorists wishing to learn about a mathematical theory providing a correct framework for the classical method of dynamic programming as well as mathematicians interested in new methods for first-order nonlinear PDEs. The work may be used by graduate students and researchers in control theory both as an introductory textbook and as an up-to-date reference book
On the vanishing viscosity approximation of a time dependent Hamilton - Jacobi equation
No full textWe prove a new comparison result for monotone viscosity solutions of Hamilton-Jacobi equations. In combination with the classical vanishing viscosity method this allows us to prove existence and uniqueness of solution for Cauchy-Dirichlet problems
A set oriented approach to global optimal control
No full textWe describe an algorithm for computing the value function for 'all source, single destination' discrete-time nonlinear optimal control problems together with approximations of associated globally optimal control strategies. The method is based on a set oriented approach for the discretization of the problem in combination with graph-theoretic techniques. The central idea is that a discretization of phase space of the given problem leads to an (all source, single destination) shortest path problem on a finite graph. The method is illustrated by two numerical examples, namely a single pendulum on a cart and a parametrically driven inverted double pendulum
Fully nonlinear elliptic equations with Keller-Osserman absorption terms - Talk at: III Workshop on Trends in Nonlinear Analysis. Dipartimento di Matematica e Informatica, Università di Cagliari. September 7 - 10, 2017
No full textSettings.
Boundary blow-up solutions of uniformly elliptic equations, in collaboration with A. Mohammed, Ball State University.
Entire solutions of degenerate elliptic equations, in collaboration with I. Capuzzo Dolcetta and F. Leoni, Sapienza Università di Roma
A short proof of the --regularity of viscosity subsolutions for superquadratic viscous Hamilton-Jacobi equations and applications
No full textRecently I.~Capuzzo Dolcetta, F.~Leoni and A.~Porretta obtain a very surprising regularity result for fully nonlinear, superquadratic, elliptic equations by showing that viscosity subsolutions of such equations are locally Hölder continuous, and even globally if the boundary of the domain is regular enough. The aim of this paper is to provide a simplified proof of their results, together with an interpretation of the regularity phenomena, some extensions and various applications
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